Journal
ANNALES DE L INSTITUT FOURIER
Volume 69, Issue 5, Pages 2037-2066Publisher
ANNALES INST FOURIER
DOI: 10.5802/aif.3288
Keywords
OT manifold; de Rham cohomology; twisted cohomology; spectral sequence; number field; LCK metric
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Funding
- Ministry of Research and Innovation, CNCS - UEFISCDI, within PNCDI III [PN-III-P4-ID-PCE-2016-0065]
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Oeljeklaus-Toma (OT) manifolds are complex non-Kahler manifolds whose construction arises from specific number fields. In this note, we compute their de Rham cohomology in terms of invariants associated to the background number field. This is done by two distinct approaches, one by averaging over a certain compact group, and the other one using the Leray-Serre spectral sequence. In addition, we compute also their twisted cohomology. As an application, we show that the low degree Chern classes of any complex vector bundle on an OT manifold vanish in the real cohomology. Other applications concern the OT manifolds admitting locally conformally Kahler (LCK) metrics: we show that there is only one possible Lee class of an LCK metric, and we determine all the possible twisted classes of an LCK metric, which implies the nondegeneracy of certain Lefschetz maps in cohomology.
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